Gamma cameras: components and systems Two Types of Tomography

detector

source

CT: Transmission Nuclear: Emission Radiation Energy Considerations

X-ray CT • We want photons with differential absorption in tissue and complete absorption in the detectors

Nuclear Medicine • We want photons with no absorption in tissue and complete absorption in the detectors • This implies higher photons energies in nuclear medicine and thicker detectors • Difficult to have internal bremsstrahlung sources, so we use nuclear sources that provide photons by radioactive decay Basics of radiation emission and detection Types of Radiation

• Neutrons • Heavy Ions • Alpha radiation: He nuclei, (2p 2n) from the alpha decay of heavy elements • Beta radiation: Electrons & positrons from neutron conversion inside the nucleus or atomic electron ejection • Gamma radiation: High energy photons (electromagnetic radiation) from de-excitation of a nucleus (usually) following other nuclear decay • Annihilation photons: High energy photons from electron + positron annihilations • x-rays: High energy photons from bremsstrahlung, caused by acceleration of a charged particle (not produced by radioactive decay) Nuclear Stability and Decay

Z = N Neutron-poor decay to ‘line of stability’ is by 100 positron emission (or EC) p+ n e+ 80 → + +ν

60 Z

40

Neutron-rich 20 decay is by beta emission n → p+ + e− +ν Z N 20 40 60 80 100 120 140 160 Decay Modes when there are too many protons for the number of neutrons

• Positron emission: a proton converts to a neutron and emits a positron (to conserve charge) p+ → n + β + + v A A + or Z X → Z −1 X + β + v 18 18 + for example: 9 F → 8 O + β + v The positron then combines with a free electron and annihilates, producing 2 annihilation photons of 511 keV each β + + e− → 2 × (E = mc2 )

• Electron capture: an orbital electron (typically from inner K or L shells) combines with a proton to form a neutron p+ + e− → n + v and also typically generating a characteristic x-ray Positron Emission and Annihilation

18 18 F O 2 n p n p E = mc p np p np p np p np = 511 keV n pp n n np n n pp n n np n pn n p n p pn n p n p np p np n β+

~2 mm e-

~180 deg Decay by Isomeric Transition

• Atoms with the same Z and A (i.e., the same nuclide) but different energy levels are called isomers • A radionuclide may decay to a more stable (lower) energy level of the same nuclide • Excess energy is released as gamma rays example 99 99m − 42 Mo → 43Tc + β + vβ (electron decay) 99m 99 43Tc → 43Tc + γ (at 140 keV) (isomeric transition)

• There are other modes of radioactive decay (e.g. fission), but they are not used in medical imaging Decay by Isomeric Transition

140 keV gamma ray Spontaneous Radioactive Decay Law

• Assume the number of spontaneous radioactive decays per unit time is proportional to the number of radioactive atoms N Thus dN = −λN N(t) = N(0)e−λt dt where λ is the radioactive decay constant • We define activity A(t) as the number of decays/time dN(t) A(t) = dt • This leads to the exponential radioactive decay law

A(t) A(0)e−λt =

A(0) −λT1/2 with a half-life defined by A(T1/2 )  = A(0)e 2 Common Radionuclides

• Half-life is important for the timing of bio- distribution and imaging • Typical half-lives are on the order of minutes to several hours • Because of the short time requirement, some

radiotracers are made Photon Energy (keV) on-site in generators or cyclotrons, while others are ordered from a 2 x 511 (for all) nearby radiopharmacy Radiotracers • Suitable radionuclides are selected based on – high enough photon energy to exit body, but low enough to be detected: Typically 100 to 500 keV – half-life of a few hours – 'clean' photon-emission decay, i.e. no alpha and beta particles, which add radiation dose • The radiotracer (ligand + radionuclide) must have suitable biodistribution, clearance, and be safe in 'trace' amounts

• Example 99mTc-labelled sestamibi for myocardial (cardiac muscle) 99mTc- sestamibi blood perfusion imaging

Detection: Interactions of high energy photons with matter

• Photoelectric effect

• Compton scattering

• Pair production

• Coherent (Rayleigh) scattering (typically ignore) Interaction of Radiation with Matter - 1

Charged particles (α and β) • Deposit energy by scattering, i.e. electromagnetic interactions with atomic electrons in the medium through which they are traveling. Many atoms along the particle track are ionized. • ‘Range’ in matter depends on energy and material characteristics (e.g., Z and density) • For β particles with kinetic energies relevant to nuclear medicine, the typical range is rather short (≤ 1mm, and much less for α particles)

• Positrons (β+ particles ) lose energy (slow down) like β- (electrons), but then annihilate in collision with an atomic electron This produces a pair of 511 keV annihilation photons traveling in opposite directions Interaction of Radiation with Matter - 2

Photons (γ annihilation photons and x-rays)

• Photons are ‘particle-like’ manifestation of electromagnetic wave packets • Interaction mechanisms for photons: – Photoelectric absorption interaction with an atomic e- – Compton scatter interaction with ‘free’ e- – Rayleigh (coherent) scatter interaction with entire atom – Pair production produces e+ - e- pair Photoelectric effect An atomic absorption process in which an atom absorbs all the energy of an incident photon.

Z 3 Z is atomic number of the material, E is energy PE∝ 3 of the incident photon, and ρ is the density of E ρ the material.

From: Physics in Nuclear Medicine (Cherry, Sorenson and Phelps)

Compton scatter

• Collision between a photon and a loosely bound outer shell orbital electron • Interaction looks like a collision between the photon and a free electron

From: Physics in Nuclear Medicine (Cherry, Sorenson and Phelps) Pair production

Occurs when a photon interacts with the electric field of a charged particle. Usually the interaction is with an atomic nucleus but occasionally it is with an electron.

Photon energy is converted into an electron-positron pair and kinetic energy. Initial photon must have an energy of greater than 1.022 MeV.

Positron will eventually interact with a free electron and produce a pair of 511 keV annihilation photons. Coherent or Rayleigh scatter

Scattering interactions that occur between a photon and an atom as a whole

Because of the great mass of an atom very little recoil energy is absorbed by the atom and photon is deflected with essentially no loss of energy

Coherent scattering is only important at energies < 50 keV Attenuation

Under conditions of narrow beam geometry the transmission of a monoenergetic photon beam through an absorber is described by an exponential equation: I(x) =I(0)e−µx where I(0) is the initial beam intensity, I(x) is the beam intensity transmitted through a thickness x of absorber, and µ is the linear attenuation coefficient of the absorber at the photon energy of interest.

The linear attenuation coefficient is expressed in units of cm-1

Note that attenuation is not the same as absorption

Attenuation coefficients

There are typically three components to the linear attenuation coefficient:

• µτ due to the photoelectric effect • µσ due to Compton scattering • µκ due to pair production

The transmitted number of photons versus thickness, x, can be written as:

I(x) = I(0)e−(µτ +µσ +µκ )x

Attenuation Coefficient

Linear attenuation coefficient µl depends on photon energy depends on material composition depends on material density dimensions are 1/length (e.g., 1/cm, cm-1)

Mass attenuation coefficient µm µm = µl /ρ (ρ = density of material yielding µl ) does not depend on material density dimensions are length2/mass (e.g., cm2/g) Water mass attenuation coefficients Example Calculation What fraction of 140 keV photons will escape unscattered from the middle of a 30 cm cylinder?

The photons must travel through 15 cm of water.

-µx -(0.15/cm)(15cm) I/I0 = e = e = 0.105 = 10.5% Radiation Detectors Types of Radiation Detectors

• Gas-filled detectors • Solid-state (semiconductor) detectors • Organic liquid scintillators • Film • Inorganic scintillators

Dose calibrator Inorgranic Scintillators

• crystalline solids • scintillate because of characteristics of crystal structure • impurities often required for scintillation properties

From: Society of Nuclear Medicine: Basic Science of Nuclear Medicine CD Inorganic scintillators

NaI(Tl) BGO LSO(Ce) GSO(Ce) Density (gm/cm3) 3.67 7.13 7.4 6.71 IMPACTS: Effective Atomic Number 51 75 66 59 Sensitivity

Attenuation Coefficient (@ 511 keV, cm-1 ) 0.34 0.955 0.833 0.674 Light Output (photons/Mev) 40K ~8K ~30K ~20K Eng and spat res Decay Time 230 ns 300 ns 12 ns 60 ns Counting speed 40 ns Wavelength 410 nm 480 nm 420 nm 430 nm Index of Refraction 1.85 2.15 1.82 1.85 Photo-sensor / Cost Hygroscopy yes no no no Rugged no yes yes no Scintillation Detection

optical photons (~ 1eV)

high energy current photon pulse for each UV photon detected

• Inorganic scintillator photomultiplier • e.g. NaI or BGO tubes (PMTs) • Dense yet transparent gain of ~ 105-106 Photomultiplier Tube

From: Physics in Nuclear Medicine (Cherry, Sorenson and Phelps) Time and energy spectra

From: Physics in Nuclear Medicine (Sorenson and Phelps) Energy Resolution

From: Physics in Nuclear Medicine (Sorenson and Phelps) Nuclear Medicine Imaging Systems Nuclear Medicine Imaging Systems

• photon source • attenuation by patient imaging equation • detectors

Components: • Collmator – A 1-2 inch thick slab of lead with holes – Allows only photons traveling in desired direction to pass through – Most common type is the is the parallel-hole collimator – Needed to generate a useful imaging equation • Scintillators – based on the property of certain crystals to emit light photons (scintillate) after deposition of energy in the crystal by ionizing radiation Collimators

• Formed from folded lead foil Nuclear Medicine Imaging Systems

• Scintillators – based on the property of certain crystals to emit light photons (scintillate) after deposition of energy in the crystal by ionizing radiation – Most commonly used scintillation crystal in nuclear instrumentation is sodium iodide with 'thallium doping', written NaI[Tl] – scintillation crystals in a gamma camera are typically 10 to 25 inches in diameter (or rectangular) and are 1/4 to 1 inch thick – Like the screens that are used in projection radiography, thicker crystals stop more photons than thinner crystals, but they also have poorer resolution Nuclear Medicine Imaging Systems

• Photomultiplier Tubes (PMTs) – Convert light flash from scintillator into a measurable electronic signal – Act as both a converter and an amplifier – light photon ejects an electron via the photoelectric effect – the electron is accelerated via increasing voltages on 'dynode' plates – each collision with a dynode releases a cluster of 3-4 electrons that are also accelerated – after 10-14 dynodes there is an amplification factor of ~106

hexagonal PMT array

20 in diam scintillator crystal Scintillator and Photomultiplier Tube assemblies

Flat plate Curved plate

wires

PMTs

NaI(Tl) scintillator

• In these photos, collimators would be placed at the bottom Nuclear Medicine scanners

'single-head' scanner

'dual-head' scanner - twice the sensitivity - more expensive Nuclear Medicine Imaging Systems

• Position estimation – based on 2-D centroid calculation – called Anger logic or Anger camera PMT signal PMT

Position

optical photons

Scintillation Collimator

gamma-ray Nuclear Medicine Imaging Equation

• To estimate activity concentration, we want photon fluence, not intensity (intensity = fluence x energy) • Photon fluence on detector at distance r from source with activity A is φ = A 4πr2 d A r • With attenuation φd = exp − µ(s,E)ds 4πr2 { ∫0 }

• With collimation and a distributed source A(x,y,z) we have for the fluence at each detector location 0 A(x, y,z) r φd (x, y) = exp − µ(x, y,z′,E)dz′ dz ∫−∞ 4πz2 { ∫0 } which is actually quite complicated due to the depth-dependent attenuation Depth-dependent attenuation

y collimator PMTS l

patient radiotracer uptake and A(x,y) source location attenuation

ray collimated line x (l) of response (x´,y) attenuation length

R scintillator signals to electronics • Imaging equation R A(x, y) R φ(l) = exp − µ(x′, y,E)dx′ dx ∫−∞ 4π(x − R)2 { ∫x } • In other words, if the patient is flipped w.r.t. to the detector, i.e. x -> -x, then we get a different photon flux φ(l) projection Collimator Blurring

• Scintigraphy (or gamma camera imaging) resolution is determined by intrinsic detector resolution and collimator blurring • Smaller/longer collimator holes improve resolution but reduce fluence (sensitivity) • For a parallel-hole collimator (most common) resolution is

expressed as FWHM, RC d R (z) = (l + b + z ) C l • Note depth (z) dependence

• Since FWHM = RC (z) = 2σ 2ln(2) so the collimator PSF is 2 2 2 hC (x, y;z) = exp{−4(x + y )ln(2) / RC (z)} Nuclear Medicine Imaging Systems

• 18-year-old male presented with low back ache since 1 year. The patient had scoliosis. Typical plain X-ray was done and was inconclusive. 99mTc-MDP bone scan was ordered to evaluate • Planar images revealed a focal solitary lesion in the L3 vertebra • A CT scan was performed to precisely localize the lesion and to confirm the diagnosis of an osteosclerotic lesion

Anterior view Posterior view Analogies with X-ray Imaging

X-rays Nuclear medicine – photon formation – photon formation • bremsstrahlung • positron emission • characteristic x-rays • isomeric transition – attenuation by tissues – attenuation by tissues • photoelectric absorption • photoelectric absorption • Compton scatter • Compton scatter – detection systems – detection systems • scintillators • scintillators – 2-D projection imaging – 2-D projection imaging • radiographs • scintigraphs – tomographic imaging – tomographic imaging • CT • SPECT and PET • collect projections from around • collect projections from around the patient the patient